Physics of Hot, Dense Plasmas David Attwood University of California, Berkeley

Hot-dense plasmas radiate in the EUV/x-ray range 𝜔 𝑝 2 = 𝑒 2 𝑛 𝑒 𝜀 0 𝑚 𝜔 𝑐 = 𝑒𝐵 𝑚 𝑛 𝑐 = 𝜀 0 𝑚 𝜔 2 𝑒 2               8.112a

Processes in a plasma Particle-particle interactions (short-range “collisions”) Kinetic theory (velocity distribution function) Collective motion (electron and ion waves) Wave-particle interactions (collisionless damping and growth) Wave-wave interactions (linear and non-linear) Continuum emission Atomic physics of ionized species (multiple charge states) Density and temperature Spatial profiles Time dependence

Understanding hot-dense plasmas requires theory, computations and experiments

Plasma theories address physical phenomena at various levels of “particle detail”

Plasma theory

The velocity distribution function, f(v)

Waves in a plasma

Wave-particle interactions

Linear and non-linear processes: scattering as an example

Plasma modeling

X-ray and EUV emission from a hot-dense plasma

Line and continuum radiation from a hot-dense plasma

Blackbody radiation: the equilibrium limit

Line and continuum radiation

Emission spectra from a xenon plasma

Ionization “bottlenecks” limit the number of ionization states present in a plasma Courtesy of J. Scofield, LLNL

Plasma theories address physical phenomena at various levels of “particle detail”

Microscopic description of a plasma

Theoretical description of a plasma

Microscopic description of a plasma (continued)

The kinetic description of a plasma

The collisionless Maxwell-Vlasov equations

A kinetic effect: Landau damping or Landau growth

Fluid description of a plasma – two approaches

Theoretical description of a plasma (continued)

The continuity equation for conservation of mass or particles

Conservation of momentum: A force equation for a fluid plasma

Conservation of momentum: A force equation for a fluid plasma (continued)

The conservation of energy for a plasma fluid

The conservation of energy for a plasma fluid (continued)

Summary of fluid equations for an isotropic, collisionless plasma

Electron-acoustic wave in a plasma

Electron-acoustic wave in a plasma (continued)

Electron-acoustic wave: dispersion relation

Electron-acoustic wave: dispersion diagram

Transverse electromagnetic waves in a plasma

Transverse electromagnetic waves in a plasma (continued)

Transverse electromagnetic waves in a plasma (continued)

Propagation in an overdense plasma

Propagation in an overdense plasma (continued)

Refractive index of a plasma

Phase velocity and group velocity

Phase velocity and group velocity (continued)

Collisional absorption of a transverse wave in a plasma

Waves in a magnetized plasma

Non-linear processes in a plasma

Linear and non-linear processes: scattering as an example

Stimulated Brillouin and Raman scattering of intense laser light

Stimulated Raman backscattering at Ne ≅ nc/4

Very hard x-rays can be generated by intense laser radiation

Continuum radiation and blackbody spectra

Blackbody radiation

Blackbody radiation across a surface

Blackbody radiation: the equilibrium limit

Three channel soft x-ray streak camera

Conventional streak camera R. Kienberger and F. Krausz, Attosecond Metrology Comes of Age, Physica Scripta, T110, 32 (2004)

IR laser field/ photoelectron streak camera Attosecond Streak Recorder (ATR): R. Kienberger and F. Krausz, Attosecond Metrology Comes of Age, Physica Scripta, T110, 32 (2004)

Multiple ionization states result in many emission lines

Soft x-ray emission spectra from a laser produced plasma

Courtesy of R. Kauffman, LLNL He-like and H-like emission lines from a laser irradiated glass (Si 𝐎 𝟐 ) disk 3 x 10 14 W/ cm 2 2 nsec Type equation here. Courtesy of R. Kauffman, LLNL

Laser irradiated titanium disk 2 joules of helium-like emission at 4.7 keV, from a 3 KJ, 600 psec irradiation Courtesy of D. Matthews, LLNL

Ionization “bottlenecks” can limit the number of ionization states present in a plasma

R. Kelley: atomic and ionic spectral lines

Stimulated Raman backscattering at Ne ≅ nc/4

Electron energy distribution showing a heated electron tail Nd,1.06 μm v os /v th = 0.53 L = 127λ Courtesy of K. Estabrook, W. Kruer and B. Lasinski, LLNL

Suprathermal x-rays at three laser wavelengths Lawrence Livermore National Laboratory

Exteme Ultraviolet (EUV) Lithography Step and scan system, Mo/Si coated optics at 13.5 nm wavelength, CO2 laser irradiated 30 μm Sn microspheres Anticipated market entry for high volume manufacturing at the “7 nm node”, likely in 2018. Courtesy of V. Banine (ASML) and W. Kaiser (Zeiss)

Searching for a plasma source for EUV lithography: The comparative spectra of Xe and Sn

Comparison of Nd and 𝐂𝐎 𝟐 laser produced plasmas Courtesy of M. Richardson, U. Central Florida

Liquid Sn droplets for EUV lithography 28 μm diameter Sn droplets 10 psec Nd prepulse 10 nsec CO 2 heating pulse Courtesy of M. Nakano, Gigaphoton